Work

A Couple of Shockers:

Undoubtedly, you have been taught that "Work equals force times
distance." Brace yourself. Work is sometimes force times
distance, but not always. Work is more subtle than
that, and in order to understand energy, you have to understand work
to a greater depth.

If you think that "work equals force times distance," then you
probably think that you automatically do work every time you exert a
force. That's not true, either!

Why? Well, the work/energy
equation says that work done (by the net force on an object)
equals the object's change in kinetic energy. More simply:

Work = Change in Kinetic Energy

This means that if an object's kinetic energy doesn't change, then
no work has been done on the object - whether or not a force has been
exerted.

In the diagram above, the green
block is moving to the right. The
red force F1 does work on the
block because it has a component
in the direction of motion. The blue
force F2 does NOT do work on the block, because it
does not have a component in the direction of motion.

Now, remember that forces cause accelerations (Newton's
Second Law), but an object can accelerate by

speeding up, in which case the object's kinetic energy
increases,

slowing down, in which case the object's kinetic energy
decreases,

or changing direction, in which case the object's kinetic
energy does not change.

So, an object's kinetic energy will only change if the force
acting on the object changes the object's speed. This will only
happen if there is a component of the force in the direction that the
object moves.

Therefore, a force will do work only
if the force has a component
in the direction that the object moves.

Calculating work can get, well, interesting. Fortunately for the
Physics 1 student, you only need to be able to calculate work done by
a force in the four simple cases shown
below. For the more mathematically mature, there is a formula that you can use to calculate the work done by a
constant force. Some of the following pages discuss calculating
work done by a variable force, but that is for AP Physics
students.

Calculating the Work Done by a Constant
Force:

In Physics 1, you need to be able to calculate the work done by a
force in four situations:

Situation:

Example:

Work done by the force F is:

The direction of the force is
in the same direction the object
moves.

The force pushing a car along a road

Force x distance

The direction of the force is in
the directionopposite the object's direction of motion.

The direction of the force is
perpendicular to the direction the
object moves.

The gravitational force the Earth exerts on the
Moon

0

The object doesn't
move.

The force you exert when pushing on a wall

0

Why?

The Key to Understanding:

The Work/Energy Equation says
that the work done on an object (by the net force on it) equals its
change in kinetic energy. So, to figure out how much work is done on
an object, just calculate the change in its kinetic energy...

If the Force Acts in the Direction That the Object Moves:

This force will tend to increase the object's speed. If the
object's speed increases, then its kinetic energy will increase. If
the kinetic energy increases, the change in kinetic energy will be
positive. Since the Work/Energy Equation guarantees that the work
done equals the change in kinetic energy, the work done must be
positive. A numerical example is
available.

If the Force Acts in the Direction Opposite to
the Direction the Object Moves:

In this situation, the force tends to slow the object down,
thereby decreasing its kinetic energy. If the kinetic energy
decreases, then the change in kinetic energy is negative. Since the
work done equals the change in kinetic energy, the work done by this
force must be negative.

There are a couple of ways to handle this:

Remember that work = - force x distance in this case. So if a
force of 5 Newtons acts on an object for a distance of 5 meters,
and the direction of the 5 Newton force is opposite to the
direction the object moves, then work done = - force x distance =
-(5 Newtons)(2 meters) = -10 Joules.

Keep in mind that direction matters with force and distance.
If the direction of the force is opposite to the direction that
the object moves, one or the other of them is acting in the
negative direction. If you do this, then work = force x distance
in this case also. In the previous example, you would say work
done = force x distance = (- 5 Newtons)(2 meters) = -10
Joules.

It really doesn't matter which method you use - just be
consistent, and remember that if the direction of the force is
opposite to the direction the object moves, the work done by the
force is negative. A numerical
example is available.

If the Force is Perpendicular to the Direction That the Object
Moves

In this case, the force does not change the speed of the object -
just its direction. Since the object's speed doesn't change, its
kinetic energy doesn't change. If the change in kinetic energy is 0,
the work done on the object is 0, too.

If the Object Doesn't Move

Work is not always force x distance, but work always involves
motion of some sort. No distance - no work.

Work is NOT Force!

Many beginning physicists confuse "exerting a force" with "doing
work." As seen above, you have to change the kinetic energy of an
object in order to do work on it - just pushing on it isn't enough.
Even the fact that you may get tired - even exhausted - holding a
heavy box or pushing on a wall, if the kinetic energy of the box or
the wall doesn't change, you didn't do work. "Exerting a force" is
NOT the same as "doing work!"